Question

In ABC, If BC=AB and $\angle B={80}^{\circ }$, then $\angle A$ is equal to:

• A. ${80}^{\circ }$
• B. ${40}^{\circ }$
• C. ${50}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is C ${50}^{\circ }$

$BC=AB$

$\Rightarrow \angle A=\angle C$ (As angles opposite to equal side are equal)

let thte angles be $x$ each.

Now by angle sum property

$\angle A+\angle B+\angle C={180}^{\circ }\Rightarrow x+{80}^{\circ }+x={180}^{\circ }\Rightarrow 2x={180}^{\circ }-{80}^{\circ }\Rightarrow 2x={100}^{\circ }\Rightarrow x={50}^{\circ }\therefore \angle A={50}^{\circ }$